Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads
d2φ/dx2 = ρ(x)/ε
Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?
I am using the Finite Difference Method to solve Poisson's equation
\frac{\partial \phi}{\partial z^2} = \frac{\rho}{\epsilon}
To do it is discretized according to the Finite Difference Approximation of the second order derivative yielding the following set of equations for each grid point...
I want to solve the Poisson equation for a thin slab of charge held above a grounded plane at z=0. The problem is somewhat reminiscent of the classical image problem of a point charge above an infinite grounded plane but differs because we are using a slab of charge instead which extends above...
I am having some trouble understanding the physics behind the formation of Schottky Barriers. According to the convential theory, the idea is that for an n-type semiconductor the electrons in the conduction band can lower their energy by filling empty states in the metal. This in turns creates a...
Suppose I want to solve the Schrödinger equation numerically for some potential V(x). The easiest way to do so, is to discretize it on a grid of finite length, and apply a finite difference scheme to approximate the second order derivative. Doing so yields an eigenvalue equation on matrix form...
I am simulating a system, where I have a semiconductor with a charge distribution in the conduction band coupled to a metal. I want to calculate the electrostatic potential due to this charge distribution but some things are confusing me. To calculate the electrostatic potential I solve Poissons...
In solid state physics you can calculate the band structure of a material, which is effectively the dispersion E_n(k), which depends on the wavevector as well as the band index. What I don't understand is this: Which states are occupied in a band? With this I mean: Which k values correspond to...
Okay so when I write a Hamiltonian on the form:
H = p2/2m* + SO + MAGNETIC FIELD
Is this equivalent to starting from the k dot p method and applying second order perturbation theory? (as you do in the case where you want to derive the effective mass hamiltonian without the SO and magnetic...
Often I see people using an effective mass model to describe electrons in the bottom of the conduction band.
Spin orbit is then included as a perturbation in this effective mass model. But what is the justification for using this sort of model?
Would the correct way not be to start from the full...
Suppose I want to solve the 1D, time-independent Schrödinger-equation for a metal-semiconductor junction.
In the metal region the Schrödinger equation reads:
(p^2/2m + V)ψ = Eψ
In the semiconductor region the Schrödinger equation reads:
(p^2/2m* + V + ΔESM)ψ = Eψ
My question is: Is there a...
Suppose I want to solve the time-independent Schrödinger equation
(ħ2/2m ∂2/∂x2 + V)ψ = Eψ
using a numerical approach. I then discretize the equation on a lattice of N points such that x=(x1,x2,...,xN) etc. Finally I approximate the second order derivative with the well known central difference...
Poissons equation for the electrostatic potential is:
∇2φ = -ρ/ε
My question is simple: If φ=0 at a point (x,y,z) can we then conclude also that ρ is zero at that point?
Can anyone explain in simple terms what the term screening means? My intuition is that a metal is a good screener because in the presence of an external electric field its free electrons will rearrange themselves such that the electric field is zero inside the metal.
But I am having a hard time...
Suppose I am given some 1D Hamiltonian:
H = ħ2/2m d2/dx2 + V(x) (1)
Which I want to solve on the interval [0,L]. I think most of you are familiar with the standard approach of discretizing the interval [0,L] in N pieces and using the finite difference formulas for V and the...